Question

Tartan Industries currently has total capital equal to $9 million, has zero debt, is in the 25% federal-plus-state tax bracket, has a net income of $2 million, and distributes 40% of its earnings as dividends. Net income is expected to grow at a constant rate of 4% per year, 250,000 shares of stock are outstanding, and the current WACC is 13.50%.

The company is considering a recapitalization where it will issue $3 million in debt and use the proceeds to repurchase stock. Investment bankers have estimated that if the company goes through with the recapitalization, its before-tax cost of debt will be 9% and its cost of equity will rise to 16.5%.
a) hat is the stock's current price per share (before the recapitalization)? Do not round intermediate calculations. Round your answer to the nearest cent. $
b) Assuming that the company maintains the same payout ratio, what will be its stock price following the recapitalization? Assume that shares are repurchased at the price calculated in part a. Do not round intermediate calculations. Round your answer to the nearest cent. $

Answer 1

The current stock price per share (before the recapitalization) is $50.53. The stock price following the recapitalization, assuming the same payout ratio, is $70.92.

Step-by-step explanation:

In order to calculate the stock price before the recapitalization, we first need to determine the earnings per share (EPS). EPS is calculated by dividing the net income by the number of shares outstanding. In this case, the net income is $2 million and there are 250,000 shares outstanding, so the EPS is $8 per share.

The stock price before the recapitalization can be calculated using the price/earnings ratio (P/E ratio). The P/E ratio is determined by dividing the stock price by the earnings per share. Given that the net income is expected to grow at a constant rate of 4% per year, we can use a constant growth model to calculate the stock price. The constant growth model is expressed as P/E ratio = (1 - Payout ratio) / (Required return on equity - Growth rate). In this case, the payout ratio is 40% and the required return on equity (WACC) is 13.50%.

Using the formula, the P/E ratio is calculated as follows:

1. P/E ratio = (1 - 0.40) / (0.1350 - 0.04)
2. P/E ratio = 0.60 / 0.0950
3. P/E ratio = 6.316

To calculate the stock price before the recapitalization, multiply the P/E ratio by the earnings per share:

1. Stock price before recapitalization = P/E ratio * EPS
2. Stock price before recapitalization = 6.316 * $8
3. Stock price before recapitalization = $50.53

Therefore, the stock's current price per share (before the recapitalization) is $50.53.

To calculate the stock price following the recapitalization, we need to determine the new number of shares outstanding and the new earnings per share. Assuming the company maintains the same payout ratio, the new number of shares outstanding can be calculated by dividing the total capital after the recapitalization by the stock price before the recapitalization. In this case, the total capital after the recapitalization is $9 million and the stock price before the recapitalization is $50.53, so the new number of shares outstanding is 178,072 shares.

The new earnings per share can be calculated by dividing the net income by the new number of shares outstanding. Using the net income of $2 million and the new number of shares outstanding of 178,072 shares, the new earnings per share is $11.23.

Finally, the stock price following the recapitalization can be calculated using the new earnings per share and the same P/E ratio as calculated before:

1. Stock price following recapitalization = P/E ratio * New EPS
2. Stock price following recapitalization = 6.316 * $11.23
3. Stock price following recapitalization = $70.92

Therefore, the stock price following the recapitalization, assuming the company maintains the same payout ratio, is $70.92.